Type Inference for First-Class Messages with Feature Constraints

We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for first-class
messages. OF extends traditional systems of feature constraints by a
selection constraint ``by first-class feature tree'' $x langle y
angle z$,
in contrast to the standard selection constraint $x[f]y$
``by fixed feature'' $f$. We investigate the
satisfiability problem of OF and show that it can be solved in
polynomial time, and even in quadratic time in an important special
case. We compare OF with Treinen's constraint system EF of feature
constraints with first-class features, which has an NP-complete
satisfiability problem. This comparison yields that the
satisfiability problem for OF with negation is NP-hard. Based on OF
we give a simple account of type inference for first-class messages
in the spirit of Nishimura's recent proposal, and show that it has
polynomial time complexity: We also highlight an immediate extension
that is desirable but makes type inference NP-hard.